Dynamical Consensus of Second-order Multi-agent Systems in Cooperation-competition Network with Markov Jumping Delays

This paper investigates the dynamical consensus problem of second-order multi-agent systems subject to Markov jumping delays. In this study, agents not only collaborate but also compete with each other, which is ubiquitous in real-world scenarios. Antagonistic interactions of the agents are considered, and modeled as negative weights on the communication graph. We first derive sufficient conditions for consensus in terms of matrix inequalities. Thereafter, a cone complementarity linearization (CCL) based algorithm is proposed for the delay-dependent controller design. The method's framework is formulated in sampled-data settings, to be more realistic and applicable. A numerical example is provided to illustrate the effectiveness of the proposed approach.